Make bezier cuves follow/face/parallel to the mesh to make hair
You can do this by controlling the Tilt property on a per vertex basis.

It may be tedious will require some manual work if it is a lot of hair.

In edit mode just select a single vertex or a whole spline at once (you can do this easily from a single selected vertex by pressing Ctrl+L) and then controlling tilt with Ctrl+T.

You may optionally turn on Proportional Edit mode and set an adequate radius to control a bunch of hair at once.